A certain prism is found to produce a minimum deviation of $38°$. It produces a deviation of $44°$ when the angle of incidence is either $42°or62°$. What will be the angle of incidence in degree when it undergoes minimum deviation?

Graph between $(\delta -i)$ for the prism: i = Angle of incidence when it is undergoes minimum deviation. From the prism formula:

$\begin{array}{l}\delta =i+e-A\\ 44=42+62-A\\ \Rightarrow A={60}^0\end{array}$

For the condition of minimum deviation $r_1+r_2=A$ (Prism formula)

$\Rightarrow r=30(\therefore r_1=r_2=r){\delta }_{\min }=2(i-r)\Rightarrow 38=2(i-30)\Rightarrow i=49$